The auto-correlation functions of AGNs and the
AGN-galaxy cross correlation function provide effective ways to study the
large scale environments of AGNs [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. Here we use the projected two-point
cross-correlation function (hereafter 2PCCF) to quantify the clustering of
our selected sample with respect to the corresponding reference galaxy sample.
The reference sample is constructed in exactly the same way
as described in [8]}, and here we provide a brief description
about the construction. The reference sample is a
magnitude-limited sample selected from the NYU-VAGC sample[9]}.
It consists of 510,605 galaxies with \(r\) -band Petrosian
apparent magnitude of \(r<17.6\) , with \(-24 < M_{0.1_{r}} < -16\) ,
and with spectroscopic redshift in range \(0.01 < z < 0.2\) .
Here, \(M_{0.1_{r}}\)  is the \(r\) -band Petrosian absolute magnitude,
\(K+E\) -corrected to \(z=0.1\) .
The random sample is constructed following the method described in
[10]}. For each galaxy in the reference sample, we
duplicate it at 10 randomly-selected sky positions in the SDSS survey
area,The geometry of the survey area is described by a set
of spherical polygons, see
http://sdss.physics.nyu.edu/vagc/ [9]}.
keeping all other properties (including redshift) of the galaxy
unchanged. The resulted random sample has the same survey geometry,
the same distribution of galaxy intrinsic properties, and the
same redshift distribution as the reference sample.
The 2PCCF is statistically more robust than the auto-correlation
function, because we can use the large number of reference galaxies
to determine both the small and large scale environments of AGNs.
The 2PCCF on small scales describes the abundance of
neighboring galaxies around the selected galaxies,
and that on large scales carries information about halo bias,
thereby providing constraints on the host halo mass of
AGNs [12]}.
